One now understands the limitations of second-order statistical quantities,
such as correlation functions and power spectra, by noting that they
discard phase information. As percolation analysis demonstrated the application
of more powerful techniques allowing the identification of sheet and filamentary
structure in the large scale structure of the universe, at nearly the
same time the Minimal Spanning Tree (MST) took hold as a filament-finding
algorithm. The MST is a pattern recognition technique borrowed from
graph theory which gives an objective measure of the connectedness of a
set of points. [1]} were the first to apply the MST to galaxy
clustering using the 2-D catalog of [2]}, the 3-D catalog
of the Center for Astrophysics Redshift Survey
[3]}, and the N-body simulations
of [4]}. These authors demonstrated how markedly different both the
observational data and N-body simulations are from a Poisson distribution.
Advances in the MST technique have
been applied to Large-Scale Structure analysis by a number of other
groups in subsequent years [5]}, [6]}, [7]}, [8]}, [9]}.
The percolation and MST methods are related to Friends-of-Friends (FoF)
techniques, which were first applied to the 3-D CFA survey by
[10]}, [11]} and later to simulation data by [12]} and even
larger samples of galaxies to obtain catalogs of groups [13]}.
The FoF technique has even been expanded for use with photometric redshift
surveys of galaxies [14]}. There are additional ways to use the
Nth nearest neighbor distances to estimate the underlying density
field [15]}, . Another approach is to use all
N nearest neighbors [16]} within a Bayesian probability framework.
